Combinatorial model of ligand-receptor binding

Overview

Combinatorial model of ligand-receptor binding

The binding of ligands to receptors is the starting point for many import signal pathways within a cell, but in contrast to the specificity of the processes that follow such bindings, the bindings themselves are often non-specific. Namely, a single type of ligand can often bind to multiple receptors beyond the single receptor to which it binds optimally. This property of ligand-receptor binding naturally leads to a simple question:

If a collection of ligands can bind non-specifically to a collection of receptors, but each ligand type has a specific receptor to which it binds most strongly, under what thermal conditions will all ligands bind to their optimal sites?


Depiction of various ligand types binding optimally and sub-optimally to receptors

In this repository, we collect all the simulations that helped us explore this question in the associated paper. In particular, to provide a conceptual handle on the features of optimal and sub-optimal bindings of ligands, we considered an analogous model of colors binding to a grid.


Partially correct and completely correct binding for the image

In the same way ligands could have certain receptors to which they bind optimally (even though such ligands could bind to many others), each colored square has a certain correct location in the image grid but could exist anywhere on the grid. We have the correct locations form a simple image so that when simulating the system it is clear by eye whether the system has settled into its completely correct configuration. In all of the notebooks in this repository, we use this system of grid assembly as a toy model to outline the properties of our ligand-receptor binding model.

Reproducing figures and tables

Each notebook reproduces a figure in the paper.

Simulation Scheme

For these simulations, we needed to define a microstate, the probability of transitions between microstates, and the types of transitions between microstates.

Microstate Definition

A microstate of our system was defined by two lists: one representing the collection of unbound particles, and the other representing particles bound to their various binding sites. The particles themselves were denoted by unique strings and came in multiple copies according to the system parameters. For example, a system with R = 3 types of particles with n1 = 2, n2 = 3, and n3 = 1 could have a microstate defined by unbound_particles = [A2, A2, A3] and bound_particles = [A1, −, A2, −, A1, −] where “−” in the bound list stands for an empty binding site.

Since the number of optimally bound particles was an important observable for the system, we also needed to define the optimal binding configuration for the microstates. Such an optimal configuration was chosen at the start of the simulation and was defined as a microstate with no unbound particles and all the bound particles in a particular order. For example, using the previous example, we might define the optimal binding configuration as optimal_bound_config = [A1, A1, A2, A2, A2, A3], in which case the number of optimally bound particles of each type in bound_particles = [A1,−,A2,−,A1,−] is m1 = 1, m2 = 1, and m3 = 0. The number of bound particles of each type is k_1 = 2, k_2 = 1, and k_3 = 0. We note that the order of the elements in unbound_particles is not physically important, but, since the number of optimally bound particles is an important observable, the order of the elements in bound_particles is physically important.

For these simulations, the energy of a microstate with k[i] bound particles of type i and m[i] optimally bound particles of type i was defined as

E(k, m) = Sum^R_i (m[i] log delta[i] + k[i] log gamma[i])

where k=[k1,k2,...,,kR] and m=[m1,m2,...,mR], gamma[i] is the binding affinity, and delta[i] is the optimal binding affinity of particle of type i. For transitioning between microstates, we allowed for three different transition types: Particle binding to a site; particle unbinding from a site; permutation of two particles in two different binding sites. Particle binding and unbinding both occur in real physical systems, but permutation of particle positions is unphysical. This latter transition type was included to ensure an efficient-in-time sampling of the state space. (Note: For simulations of equilibrium systems it is valid to include physically unrealistic transition types as long as the associated transition probabilities obey detailed balance.)

Transition Probability

At each time step, we randomly selected one of the three transition types with (equal probability for each type), then randomly selected the final proposed microstate given the initial microstate, and finally computed the probability that said proposal was accepted. By the Metropolis Hastings algorithm, the probability that the transition is accepted is given by

prob(init → fin) = min{1, exp(- β(Efin −Einit))*π(fin → init)/π(init → fin) }

where Einit is the energy of the initial microstate state and Efin is the energy of the final microstate. The quantity π(init → fin) is the probability of randomly proposing the final microstate state given the initial microstate state and π(fin → init) is defined similarly. The ratio π(fin → init)/π(init → fin) varied for each transition type. Below we give examples of these transitions along with the value of this ratio in each case. In the following, Nf and Nb represent the number of free particles and the number of bound particles, respectively, before the transition.

Types of Transitions

  • Particle Binding to Site: One particle was randomly chosen from the unbound_particles list and placed in a randomly chosen empty site in the bound_particles list. π(fin → init)/π(init → fin) = Nf^2/(Nb +1).

Example: unbound_particles = [A2, A2, A3] and bound_particles = [A1, −, A2, −, A1, −]unbound_particles = [A2, A3] and bound_particles = [A1, A2, A2, −, A1, −]; π(fin → init)/π(init → fin) = 9/4

  • Particle Unbinding from Site: One particle was randomly chosen from the bound_particles list and placed in the unbound_particles list. π(fin → init)/π(init → fin) = Nb/(Nf + 1)^2.

Example: unbound_particles = [A2, A2, A3] and bound_particles = [A1, −, A2, −, A1, −]unbound_particles = [A2, A2, A3, A2] and bound_particles = [A1, −, −, −, A1, −]; π(fin → init)/π(init → fin) = 3/16

  • Particle Permutation: Two randomly selected particles in the bound_particles list switched positions. π(fin → init)/π(init → fin) = 1.

Example: unbound_particles = [A2, A2, A3] and bound_particles = [A1, −, A2, −, A1, −]unbound_particles = [A2, A2, A3] and bound_particles = [A2, −, A1, −, A1, −]; π(fin → init)/π(init → fin) = 1

For impossible transitions (e.g., particle binding when there are no free particles) the probability for accepting the transition was set to zero. At each temperature, the simulation was run for anywhere from 10,000 to 30,000 time steps (depending on convergence properties), of which the last 2.5% of steps were used to compute ensemble averages of ⟨k⟩ and ⟨m⟩. These simulations were repeated five times, and each point in Fig. 6b, Fig. 7b, Fig. 8b, and Fig. 9 in the paper represents the average ⟨k⟩ and ⟨m⟩ over these five runs.

References

[1] Mobolaji Williams. "Combinatorial model of ligand-receptor binding." 2022. [http://arxiv.org/abs/2201.09471]


@article{williams2022comb,
  title={Combinatorial model of ligand-receptor binding},
  author={Williams, Mobolaji},
  journal={arXiv preprint arXiv:2201.09471},
  year={2022}
}
Owner
Mobolaji Williams
Mobolaji Williams
History Aware Multimodal Transformer for Vision-and-Language Navigation

History Aware Multimodal Transformer for Vision-and-Language Navigation This repository is the official implementation of History Aware Multimodal Tra

Shizhe Chen 46 Nov 23, 2022
IOT: Instance-wise Layer Reordering for Transformer Structures

Introduction This repository contains the code for Instance-wise Ordered Transformer (IOT), which is introduced in the ICLR2021 paper IOT: Instance-wi

IOT 19 Nov 15, 2022
Hl classification bc - A Network-Based High-Level Data Classification Algorithm Using Betweenness Centrality

A Network-Based High-Level Data Classification Algorithm Using Betweenness Centr

Esteban Vilca 3 Dec 01, 2022
An original implementation of "Noisy Channel Language Model Prompting for Few-Shot Text Classification"

Channel LM Prompting (and beyond) This includes an original implementation of Sewon Min, Mike Lewis, Hannaneh Hajishirzi, Luke Zettlemoyer. "Noisy Cha

Sewon Min 92 Jan 07, 2023
The code of NeurIPS 2021 paper "Scalable Rule-Based Representation Learning for Interpretable Classification".

Rule-based Representation Learner This is a PyTorch implementation of Rule-based Representation Learner (RRL) as described in NeurIPS 2021 paper: Scal

Zhuo Wang 53 Dec 17, 2022
object recognition with machine learning on Respberry pi

Respberrypi_object-recognition object recognition with machine learning on Respberry pi line.py 建立一支與樹梅派連線的 linebot 使用此 linebot 遠端控制樹梅派拍照 config.ini l

1 Dec 11, 2021
Implementation of "RaScaNet: Learning Tiny Models by Raster-Scanning Image" from CVPR 2021.

RaScaNet: Learning Tiny Models by Raster-Scanning Images Deploying deep convolutional neural networks on ultra-low power systems is challenging, becau

SAIT (Samsung Advanced Institute of Technology) 5 Dec 26, 2022
VisionKG: Vision Knowledge Graph

VisionKG: Vision Knowledge Graph Official Repository of VisionKG by Anh Le-Tuan, Trung-Kien Tran, Manh Nguyen-Duc, Jicheng Yuan, Manfred Hauswirth and

Continuous Query Evaluation over Linked Stream (CQELS) 9 Jun 23, 2022
Code and data accompanying our SVRHM'21 paper.

Code and data accompanying our SVRHM'21 paper. Requires tensorflow 1.13, python 3.7, scikit-learn, and pytorch 1.6.0 to be installed. Python scripts i

5 Nov 17, 2021
Programming with Neural Surrogates of Programs

Programming with Neural Surrogates of Programs

0 Dec 12, 2021
Framework that uses artificial intelligence applied to mathematical models to make predictions

LiconIA Framework that uses artificial intelligence applied to mathematical models to make predictions Interface Overview Table of contents [TOC] 1 Ar

4 Jun 20, 2021
Game Agent Framework. Helping you create AIs / Bots that learn to play any game you own!

Serpent.AI - Game Agent Framework (Python) Update: Revival (May 2020) Development work has resumed on the framework with the aim of bringing it into 2

Serpent.AI 6.4k Jan 05, 2023
GANimation: Anatomically-aware Facial Animation from a Single Image (ECCV'18 Oral) [PyTorch]

GANimation: Anatomically-aware Facial Animation from a Single Image [Project] [Paper] Official implementation of GANimation. In this work we introduce

Albert Pumarola 1.8k Dec 28, 2022
Information-Theoretic Multi-Objective Bayesian Optimization with Continuous Approximations

Information-Theoretic Multi-Objective Bayesian Optimization with Continuous Approximations Requirements The code is implemented in Python and requires

1 Nov 03, 2021
Code to run experiments in SLOE: A Faster Method for Statistical Inference in High-Dimensional Logistic Regression.

Code to run experiments in SLOE: A Faster Method for Statistical Inference in High-Dimensional Logistic Regression. Not an official Google product. Me

Google Research 27 Dec 12, 2022
Self-Supervised depth kalilia

Self-Supervised depth kalilia

24 Oct 15, 2022
Node Editor Plug for Blender

NodeEditor Blender的程序化建模插件 Show Current 基本框架:自定义的tree-node-socket、tree中的node与socket采用字典查询、基于socket入度的拓扑排序 数据传递和处理依靠Tree中的字典,socket传递字典key TODO 增加更多的节点

Cuimi 11 Dec 03, 2022
How to Become More Salient? Surfacing Representation Biases of the Saliency Prediction Model

How to Become More Salient? Surfacing Representation Biases of the Saliency Prediction Model

Bogdan Kulynych 49 Nov 05, 2022
Code and datasets for the paper "Combining Events and Frames using Recurrent Asynchronous Multimodal Networks for Monocular Depth Prediction" (RA-L, 2021)

Combining Events and Frames using Recurrent Asynchronous Multimodal Networks for Monocular Depth Prediction This is the code for the paper Combining E

Robotics and Perception Group 69 Dec 26, 2022
Differentiable Prompt Makes Pre-trained Language Models Better Few-shot Learners

DART Implementation for ICLR2022 paper Differentiable Prompt Makes Pre-trained Language Models Better Few-shot Learners. Environment

ZJUNLP 83 Dec 27, 2022